Khan Academy: Linear Transformation Examples: Rotation in R3 Around the X Axis

Video shows how to write a transformation matrix in R^3 that rotates a vector around the x-axis. Compares the rotation matrix in R^3 to the rotation matrix in R^2 found in the previous video and discusses how it could be applied for more...

Video first shows visually that a rotation is a linear transformation. Shows how to construct a transformation matrix that will rotate a vector through a given angle. Shows both the general rotation matrix and an example of a rotation...

Expressing a Projection on to a line as a Matrix Vector prod

A video showing how any linear transformation can be represented as a matrix vector product.

Video shows an example of the image of a subset of a domain under a linear transformation. Example includes defining a triangle using vectors. [18:11]

Video shows an example of the image of a subset of a domain under a linear transformation. Example includes defining a triangle using vectors. [18:11]

Video first gives the conditions that define a linear transformation. Gives examples of determining if a transformation is linear or not. Shows several types of notation for vector transformations. [13:52]

Video shows how to define a plane in R3 using a point on the plane and a normal vector to the plane. Includes a visual representation to help understanding. [13:53]

Creating scaling and reflection transformation matrices (which are diagonal).

A video lesson that works through a concrete example to find the inverse of a 3 x 3 matrix. The original matrix is augmented by the identity matrix and then put in reduced row echelon form. The result of the row operations on the...